Mem. S.A.It. Suppl. Vol. 26, 38 Memorie della c SAIt 2014 Supplementi

The Hungaria : close encounters and impacts with terrestrial planets

M. A. Galiazzo, A. Bazso, and R. Dvorak

Institute of Astronomy, University of Vienna, Turkenschanzstr.¨ 17, A-1180 Wien, Austria e-mail: [email protected]

Abstract. The Hungaria family (Named after (434) Hungaria), which consists of more than 5000 members with semi-major axes between 1.78 and 2.03 AU and have in- clinations of the order of 20◦, is regarded as one source for Near-Earth Asteroids (NEAs). They are mainly perturbed by and , and are ejected because of and secular resonances with these planets and then become Mars-crossers; later they may even cross the of Earth and Venus. We are interested to analyze the close encounters and possible impacts with these planets. For 200 selected objects which are on the edge of the group we integrated their orbits over 100 million years in a simplified model of the planetary system (Mars to Saturn) subject to only gravitational forces. We picked out a sam- ple of 11 objects (each with 50 clones) with large variations in semi-major axis and some of them achieve high inclinations and eccentricities in connection with mean motion and secular resonances which then leads to relatively high velocity impacts on Venus, Earth and Mars. We report all close encounters and impacts with the terrestrial planets and statistically determine the mean life and the orbital distribution of the NEAs of these Hungarias.

Key words. Hungarias – asteroids – close encounters – impacts – NEAs – terrestrial plan- ets

1. Introduction In the first place this is deduced from the spec- tral type of the major component of the fam- The Hungaria group contains about 8000 as- 1 ily, the E-type or Achondritic Enstatite (about teroids, located in orbital element space be- 60%) , which is consistent with the composi- tween 1.78 < a(AU) < 2.03, e < 0.19 and ◦ ◦ tion of some meteorites (aubrites, Zellner et al. 12 < i < 31 , inside the ν6 secular reso- (1977) found on the Earth. Other Hungarias are nance (SR) and the mean motion resonances also S-type (17.2%) and less C-types (6.0%) (MMRs) 4:1 with Jupiter (J4:1) and 3:4 with (Warner et al. 2009). The objects of the group Mars (M3:4). are not very big in size compared to the other There is evidence from meteorites that Main Belt Asteroids (MBAs), they have an av- members of the Hungaria group may reach the erage diameter of 1 km ranging up to 11.4 km, terrestrial planets and be a source of impactors. (434)Hungaria being the biggest member. The

1 majority of Hungarias have a retrograde rota- following in part a suggestion of Spratt (1990), tion and similar spin rates (Pravec et al. 2008; so that our sample finally consisted of 8258 aster- Rossi et al. 2009). oids (August 2010) Galiazzo: The 39

The content of the paper is as follows: considered a close encounter when the aster- oid crosses the following distances (close en- – methods and details on the investigated counter radius, CER) from each planet: the av- bodies; erage lunar distance 0.0025 AU for the Earth, – statistical and analytical study on and the lunar distances scaled to the respec- Hungarias path to be NEAs, impacts tive Hill Sphere of the other 2 considered plan- and close encounters with the Terrestrial ets 0.00166 AU for Mars and 0.00170 AU for planets; Venus. – conclusions: discussion and summary on the previous described studies. 3. Results 3.1. Statistical analysis of the dynamics 2. Methods and details of the Hungarias’ Fugitives. Hungaria asteroids was picked up from The 11 fugitives are also inside the Hungaria the database2 of the Lowell observatory at Family, so it is possible to speak about escapers Flagstaff, then a reasonable number of aster- from the family, a more restrictive definition of oids was taken for the orbital integrations: 200 “group”; we remember here the definitions: out of the total Hungarias inside the group, the ones that have the higher deflection from the Group: a “group” of asteroids is defined by average of a metric d based on the osculating a range of osculating elements (see also q elements: d = ( e )2 + ( a )2 + ( sin i )2 Warner et al. 2009) Family: a (dynamical) “family” of asteroids (a, e and i are respectively the semi-major axis, is defined by the use of the proper ele- the eccentricity and the inclination of the aster- ments. Families are defined by a specifi- oids). cal clustering method, which gives dynam- Firstly these first sample was integrated for ically a homogeneous sample of asteroid 100 My with the Lie-integrator (Hanslmeier in the Main Belt, the most well known are & Dvorak 1984; Eggl & Dvorak 2010) the Hierarchical Clustering Method (HCM, in a simplified (planets from Zappala´ et al. 1990) and the Wavelet 3 Mars to Saturn), enough for the scope of this Analysis Method (WAM, Bendjoya et al. first work, discovering the objects which es- 1991). cape from the group: 11 bodies (see Table 1). They were discriminated considering only The of the fugitives is rather chaotic those ones who has a major deflection in the after a close encounter as it can be seen in the semi-major axis: ∆a > ∆agroup/16 = 0.01563 case of (41577) 2000 SV2 (Fig. 2). This as- AU, with ∆a = amax − amin: deviations from teroid become a Sungrazers in less than 100 the group’s mean semi-major axis of more than Myrs, crossing the ν6 secular resonance at ∼ ∼ 7% of the total width of the group. 71Myr and then after a very close encounter Secondly the 11 fugitives were integrated with Venus, it become a NEAs keeping a high again with the same initial conditions and to- value of eccentricity, always e > 0.3, finally gether with 49 clones for each one of them in- after several close encounters with all the plan- side these ranges: a ± 0.005 AU, e ± 0.003 and ets, it collides the Sun. i ± 0.005◦. This time in a Solar System which During the orbital evolution of 100 Myrs, take in accounts all the planets from Venus to all the Fugitives become Mars-crossers. 91 % Saturn, so taking in account also the terres- of them (the clones) are planet crossing as- trial planets and all the close encounters. It is teroids (PCAs) and 58% NEAs, in particu- lar Amors and Apollos: Amors are the Earth- 2 www2.lowell.edu/elgb approaching NEAs with orbits exterior to the 3 Integrations with the full Solar System from Earth’s (a > 1.0AU and 1.017(AU) < q < Mercury to Neptune shows the same general results. 1.3(AU); Apollos are Earth-crossing NEAs 40 Galiazzo: The Hungaria Asteroids

Fig. 1. The Hungaria group in the orbital space and the metric. Reddish crosses are for the asteroids with the most extreme value in the metric. with semi-major axis larger than the Earth (a > ing them. In order to make this the diameter 1.0 AU and q < 1.017 AU, q is the perihelium), of the asteroids is needed, see (Table 1). They this means that 3.2% of all the Hungarias be- are computed with the equation of Fowler & come NEAs in 100 Myrs. The average time- Chillemi (1992), which gives a quite precise evolution of the Hungarias escapers is shown results, with an error, usually of second order in Fig. 3, a Fugitive usually have a close en- (if the diameter is 220km the error is about of counter with Earth and Venus after becoming 201km, see Galiazzo 2009): D = 1329√ 10−H/5. ρv an Amor, an Apollo and an Aten. The entry velocity at the CER for each The estimates of the diameter of the planet it is 21.5 ± 2.3 km/s for the Earth, Hungaria-impactors are based on the assump- 27.8 ± 1.7 km/s for Venus and 10.8 ± 1.0 km/s tion that the asteroid has a spherical shape. for Mars. The known impact structures on Earth range from small circular bowls only a few 3.2. Impacts hundred metres in diameter to large com- plex structures more than 200 km in diameter Some singular clones have an impact with a (French 1998), with ages as old as 2 Gyr. The terrestrial planet. The percentage of the whole biggest known craters on Earth are Vredefort Hungaria’s population having an impact with a and Sudbury craters, larger than 200 km in di- terrestrial planet during 100 Myrs is: 0.7% for ameter. The “projectiles” capable of forming the Earth, 2.4% for Venus and 1.1% for Mars. craters on the terrestrial planets today come It is possible to compute the diameter of the pu- primarily from three populations(Ivanov et al. tative craters and some typical values concern- 2002a): Galiazzo: The Hungaria Asteroids 41

Fig. 2. Upper panel: semi-major axis and Planetocentric distance versus time. In blue, green and red, close encounters with respectively: Mars, Venus and Earth. Bottom panel: eccentricity (red), inclination (black) and perihelium (blue) versus time.

Fig. 3. Average time-evolution of a Fugitive. Each “x” represents 1 Myr. Atens are Earthcrossing NEAs with semimajor axis smaller than the Earth: a < 1.0 AU and Q > 0.983AU (Q is the aphelion); Atiras have the orbit contained with the one of the Earth: a < 1.0 AU and Q < 0.983 AU.

1. asteroids from the main belt ing from a < 7.4 AU orbits. Some hundreds of 2. Jupiter-family from the NEAs have a diameter ≥ 1 km similar to most 3. long period comets from the of the known Hungarias. For the found fugi- tives the diameters range from approximately Bottke et al. (2002) showed that the asteroids 1 km to ∼ 2.5 km, see Table 1. provide most of terrestrial impact craters com- 42 Galiazzo: The Hungaria Asteroids

Table 1. Absolute magnitude in visual, slope parameter,diameter (km) and spectra types of the 11 fugitives. Data from the database “astorb.dat” of the Minor Body Center. Where not data are given for the visual (ρv), the average (aver.) one, 0.38 (Warner et al. (2009), was taken. Question mark stands for no data available for the spectrum type.

Asteroid HV GD ρv Spec.-Type (211279) 2002 RN137 16.9 0.15 1.01 0.3 Xe? (41898) 2000 WN124 16.2 0.15 1.24 aver. ? (39561) 1992 QA 15.3 0.15 1.88 aver. ? (30935) Davasobel 14.7 0.15 2.48 aver. S? (175851) 1999 UF5 16.9 0.15 0.90 aver. Xe? (152648) 1997 UL20 15.8 0.15 1.49 aver. ? (141096) 2001 XB48 16.2 0.15 1.24 aver. ? (24883) 1996 VG9 15.3 0.15 1.88 aver. ? (41577) 2000 SV2 14.9 0.15 2.26 aver. ? (129450) 1991 JM 16.8 0.15 0.94 aver. ? (171621) 2000 CR58 16.2 0.15 1.24 aver. ?

3.3. Craters the values found in Ivanov et al. (2002a) for bodies with H < 17 mag, even if the value for During the integrations some clones have an Mars is very small compared to the results of impact with Terrestrial planets. The impact is this paper (0.21 compared to 0.34). This bias assumed if the body surmounts the limit for the is due to the fact that here it is used a small atmospheric entry (see Fig. 1 of Westman et al. 4 sample and restricted to a special group of as- 2003), for this cutoff it has been chosen in teroids. Averaging on the fugitives which have this work a value for the Earth equal to 65.4 impacts (9 out of 11), the average probability km. For the other planets it has been derived range from (2.20−3.49)×10−8/yr, meaning that an empirical equation using a constant k which a fugitive should orbit between 0.026 − 0.045 depends on the scale height hatm of the atmo- Gyr at its currently observed orbit before im- sphere, measured in astronomical units (1 AU pacting one of the terrestrial planets5. = 149597870.7 km) and the (surface) density The impact angle is defined via the angle of each planet (for parameters see Table 1): of the planetocentric velocity vector with the (E) (E) (E) normal to the target’s surface: k = ρ htot /hatm (1) v · n cos(θ ) = (4) where norm kvk · knk (E) (E) (E) ◦ htot = r + hatm. (2) and so θ = 90 − θnorm. The diameter of the crater by means of the equations for the tran- (E) sient crater diameter (Collins et al. 2005): Here hatm is the scale height of the Earth atmo- (E) (E) sphere, ρ the density, and r is the radius !1/3 ρi 0.78 0.44 −0.22 1/3 of the Earth (also in astronomical units). The Dtc = 1.161 Di vi g (sin θ) , (5) ρt atmospheric entry (rimp) for Venus and Mars is given by the equation: here Di is the diameter of the impactor, ρi its density (for the Hungarias we chose ρ = (P) (P) (P) i rimp = r + htot ρ /k. (3) 5 0.040 Gyr for the Earth, meaning that impacts The probabilities computed from the re- by Hungarias may happen since ∼ (0.46 − 0.92) sults of the integrations confirm the trend and Gyr ago. However this is only one of the probable suggestions, so caution may be advised before com- 4 see http://neo.jpl.nasa.gov/news/2008tc3.html pletely accepting these connections. Galiazzo: The Hungaria Asteroids 43

Earth Earth Table 2. ρ1 and ρ2 are the densities of sedimentary and crystalline rock, respectively, Venus (Collins et al. 2005); ρ1 is the (surface) densitity given by the fact sheet of NASA Venus (http://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html) and ρ2 is the upper limit of Mars basalt given in http://geology.about.com/cs/rock types/a/aarockspecgrav.htm. ρ1 is the den- sity for Mars: we have considered the lower value for andesite (see the link mentioned just be- fore). For the scale heights of the atmospheres (hatm) we have chosen for the Earth the value mentioned at http://neo.jpl.nasa.gov/news/948tc3.html. All the other parameters come from the NASA fact-sheets for each planet.

3 3 Planet radius R [km] density ρ1 [kg/m ] density ρ2 [kg/m ] pressure P [bar] hatm [km] g [m/s] Venus 6051.8 2800 3000 92 15.9 8.9 Earth 6371.0 2500 2750 1.01325 8.5 9.8 Mars 3396.2 2500 − 0.00636 11.11 3.71

3 1700 kg/m , McEachern et al. 2010), and ρt craters that range from 4 to 10 km (Condit is the density of the target. For the final crater 1978), similar to the putative crater made diameter (McKinnon & Schenk 1985) it fol- by a clone of 1996 VG9. lows: Venus: Looking at the Venus database6, also here a lot of craters has similar diameters D1.13 tc to the ones found in these studies. Dc = 1.17 0.13 , (6) D∗ The impact energy, is computed via the with D∗ the transition diameter inversely pro- portional to the surface gravity of the target equation given by Collins et al. (2005): (Melosh 1989), with the nominal value for the π 3 2 E = ρastD v (8) Moon of D∗,Moon = 18 km (Minton & Malhotra 12 ast i 2010): This is the energy equivalent in megatons (Mt) (P) D∗ = 1.62 D∗,Moon/g . (7) if we consider the impactor’s diameter Dast ex- pressed in meters, its velocity vi in km/s and Earth: Grieve & Shoemaker (1994) suggest 3 the density ρi in g/cm . As can be seen the en- that it is possible to distinguish two pop- ergy depends strongly on the diameter of the ulations of craters: (i) craters with diame- impactor and on the impact velocity, which is ters between 24 to 39 km, the oldest be- computed by the equation given in Collins et ing 115 Myr; and (ii) craters with diame- al. (2005): ters from 55 to 100 km, the oldest being 370 Myr. Ivanov et al. (2002a) assume ρiDi vi = v∞ . (9) that craters smaller than ∼ 20 km belong to 3 Ppl ρiDi + the younger set, so Hungarias should have 2 gpl sin θ formed craters younger than 115 Myr. This (using v∞ as the speed of the asteroid before the should be compared to the diameters found atmospheric entry, Di impactor diameter, Ppl from our computations (see Tables 3,4 and atmospheric pressure). The maximum impact 5), with the biggest crater formed by 2002 energy released for the Earth is ≈ 4.18 × 105 SV2 (20.89 km). Mt, more than forty thousand times the energy Mars: In the equatorial geologic-geomorphic units of Mars (latitude ≤ 35◦), there are 6 http://www.lpi.usra.edu/resources/vc/vcnames/ 44 Galiazzo: The Hungaria Asteroids released to create the Meteor Crater in Arizona, The inclination at the atmospheric entry USA (Shoemaker 1983). The impact energies looks very high for Mars and contrary for the for Venus are on average lower than on Mars. Earth, while the eccentricities continue to in- Tables 3, 4 and 5 summarize the data for crease going interiorly the solar system. The the impacting asteroids, including the energy average impact angle seems higher for the released by the “crash” of the impactor and the Earth and also the biggest craters appear here. diameter of the crater7 on the two main types The impact velocity of the fugitives found of the solid surfaces of the Earth (sedimentary for the Earth range from 14.2 to 30.18 km/s for rocks and crystalline rocks); two different the Earth. These values are larger than the re- surfaces for Venus (strong andesite and strong sults given by Ivanov & Hartmann (2002b); basalt), and one for Mars (andesite). Chyba (1993)(hvi = 19.3 km/s for an aster- For each planet they are shown the maximum oid with Hv < 17 mag and hvi = 18.6 km/s crater diameter made by the fugitives and for Hv < 15 mag), even if that sample is for the real craters on the terrestrial planets with asteroids with D < 50 m. Hungarias seem to similar diameter to the one made by the arrive faster on the average than other types of asteroids having close encounters with the Hungarias. D1 and D2 are the crater diameters for a sedimentary surface (the bigger one) and Earth. Concerning Mars the range of veloci- for crystalline surface, for the Earth; strong ties is from 9.32 to 23.42 km/s with the maxi- andesite surface (the bigger diameter) and mum value higher than for the average aster- strong basaltic surface for Venus, and only oids found in Ivanov & Hartmann (2002b), feeble andesite surface for Mars. θ is the so the Hungarias arrive faster to Mars, too. angle of impact; E, the energy released by On the other hand we find lower velocities for Venusian impactors, our results range from the impact and ENord.Cr. displays how many times we have the energy of the Nordlingen¨ 5.24 to 24.57 km/s, against the average velocity crater (the energy released by the impactor of 24.2 km/s of Ivanov & Hartmann (2002b). in the Ries Crater is ∼ 15 megatons, see Some NEOs (in the JPL Small-Body the impact database of the Planetary Space Database Search Engine) fit well with the el- Science Centre), a thousand times the en- ements of the found impactors, also inside ergy released at Hiroshima (15 kilotons, see the ranges of the and absolute mag- http://www.world-nuclear.org/info/inf52.html) nitudes of the Hungarias, spectra types gave compared to the energy released by the a good fitting, when they are present: (1620) Geographos, (2201) Oliato, (5751) Zao, (3551) Hungaria escapers. Then v∞ is the velocity at Verenia, (5604) 1992 FE, an of the atmospheric entry, vimp, the impact velocity 2.3km (Delbo´ et al. 2003). and ve is the relative escape velocity of the planet. There are also the orbital elements (a, e, i) at the border distance to be considered 4. Conclusions as a close encounter; the time of the impact t from the beginning of the integration and In 100 Myrs, 3.2% of all the Hungarias be- the disclosure time to arrive from the lunar come NEAs and among these more than 90% distance to the target (to the limit of the are PCAs. Less than 1 % of them has an im- atmospheric entry), ∆t. pact with Mars or the Earth, 2.4% of them with Venus and the rest end up as a Sun-grazer or stay still in a NEA’s orbit; very rarely they are Asteroid (152648) 1997 UL20 have the maximum number of impacts by its clones, 11 Jupiter crossers. different ones. Found Hungaria fugitives which collide a planet create craters similar to the ones present on the terrestrial planets as dimension (D < 7 All the diameters refer to an asteroid that 30km). The biggest computed craters for them does not suffer from fragmentation during its flight are 28 km for the Earth, 20 km for Venus and through the atmosphere. 23 km for Mars. Galiazzo: The Hungaria Asteroids 45

Table 3. Earth-impacts

Asteroid D1 [km] D2[km] θ 5 Energy [Mt ×10 ] ENord.Cr. v∞ [km/s] vimp [km/s] ve [km/s] semi-major axis [AU] eccentricity inclination [deg] time [Myr] ∆t [h] Earth craters Davasobel 27.47 26.61 55 4.181 15.48 15.23 16.05 11.20 0.8020 0.3918 6.10 89.182 9.5 8 9 10 Crater Diameter vimp Age [Ma] Slate Islands 30.00 ∼ 20km/s 436 −

Table 4. Venus-impacts.

Venus craters 2000 SV2 19.60 19.15 43 4.851 17.965 31.21 19.88 10.2 0.9269 0.3755 46.47 97.403 3.87 11 Crater Diameter vimp Age [Ma] Rowena 19.6 − − −

Table 5. Mars-impacts.

Mars craters 2000 SV2 22.85 53 2.689 9.958 14.57 14.80 5 12 Crater Diameter vimp Age [Ma] Endeavour 22.0 − − −

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